Finite Group Databasebeta

← #15846878

Subgroups — #15846878

Order 3328.

670 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124645C211yesmaximal, characteristic
2#13124319C211yesmaximal, characteristic
3C8×#6127C211yesmaximal, characteristic
4#13114263C214yesmaximal, complemented
5#13114256C214yesmaximal, complemented
6#13113592C211yesmaximal, characteristic, complemented
7#13113521C211yesmaximal, characteristic, complemented
8#13113508C211yesmaximal, characteristic, complemented
9C2×C13×#487C211yesmaximal, characteristic, complemented
10C2×C13×C4⋊Q8C2211yescharacteristic
11C2×C13×C4⋊Q8C2211yescharacteristic
12C2×#88196—21no—
13C4×#6127C2211yescharacteristic
14C13×#487—21no—
15C13×#487—21no—
16C13×#487C2214yes—
17C2×C13×#103—22no—
18C2×C4×C8×C13C2211yescharacteristic
19#11718886—21no—
20C8×C22⋊D13—22no—
21#11718755C2212yes—
22#11718752—21no—
23#11718751—21no—
24#11718751C2212yes—
25#11718748C2212yes—
26#11718745—21no—
27#11718744—21no—
28#11718744C2212yes—
29#11718627—21no—
30#11718625—21no—
31#11718586C2211yescharacteristic
32#11718585C2211yescharacteristic
33#11718585C2211yescharacteristic
34C8×D52C2212yes—
35#11718346—21no—
36C4×C8×D13—21no—
37C8×Dic26C2212yes—
38#11718139C2214yes—
39#11718139C2214yes—
40#11718049C2214yes—
41C22×Q8×C13—21no—
42C22×Q8×C13—21no—
43C2×#6127D411yescharacteristic
44C22×C8×C13D412yes—
45C13×C4⋊Q8—21no—
46C13×C4⋊Q8—21no—
47C13×C4⋊Q8—21no—
48C13×C4⋊Q8—21no—
49C13×C4⋊Q8—21no—
50C13×C4⋊Q8—21no—
51C13×C4⋊Q8C2312yes—
52C13×C4⋊Q8C2312yes—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—21no—
57C2×C42×C13C2311yescharacteristic
58C2×#6107—22no—
59#88196—44no—
60C2×#6106—22no—
61C4×C22⋊D13—21no—
62C4×C22⋊D13—21no—
63#88180D411yescharacteristic
64C2×#6099—21no—
65C2×#6099—21no—
66C2×C8×D13—22no—
67C4×D52D411yescharacteristic
68C4×D52C2311yescharacteristic
69#88126—21no—
70C42×D13—21no—
71C4×Dic26D411yescharacteristic
72C4×Dic26C2311yescharacteristic
73C13×#103—24no—
74C13×#103—24no—
75C4×C8×C13D411yescharacteristic
76C4×C8×C13D411yescharacteristic
77C4×C8×C13C2312yes—
78#88075—22no—
79#88075—22no—
80C22⋊#1055—21no—
81#88060—22no—
82#88054—22no—
83C8×Dic13—22no—
84#88050—22no—
85#88049—22no—
86#88048—22no—
87#88047—22no—
88C4⋊#1055—21no—
89C4⋊#1055—21no—
90C4⋊#1055C2312yes—
91C4⋊#1055C2312yes—
92C4⋊#1055C2312yes—
93C4×#1055—21no—
94#19275—131nomaximal, Sylow
95C2×Q8×C13—22no—
96C2×Q8×C13—22no—
97C2×Q8×C13—44no—
98C2×Q8×C13—41no—
99C2×Q8×C13—41no—
100C2×Q8×C13—42no—
101C2×Q8×C13—42no—
102C22×C4×C13—41no—
103C22×C4×C13—41no—
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13#4111yescharacteristic
107C2×C22⋊D13—21no—
108#6127—22no—
109#6127SD1614yes—
110C2×D52C2×D411yescharacteristic
111C2×C4×D13—21no—
112C2×C4×D13—21no—
113C2×C4×D13—21no—
114C2×Dic26C2×D411yescharacteristic
115C2×C8×C13—42no—
116C2×C8×C13C2×D412yes—
117C2×C8×C13C2×D412yes—
118C13×C4⋊C4—22no—
119C13×C4⋊C4—22no—
120C13×C4⋊C4—22no—
121C13×C4⋊C4—22no—
122C13×C4⋊C4—41no—
123C13×C4⋊C4—41no—
124C13×C4⋊C4—41no—
125C13×C4⋊C4—41no—
126C42×C13C2×D411yescharacteristic
127C42×C13C2×D411yescharacteristic
128C42×C13#4111yescharacteristic
129C42×C13C2411yescharacteristic
130C22⋊Dic13—21no—
131#6107—44no—
132#6106—44no—
133#6103—21no—
134#6103—21no—
135C4⋊Dic13C2×D411yescharacteristic
136C4⋊Dic13C2×D411yescharacteristic
137#6101—21no—
138#6101—21no—
139C4×Dic13—21no—
140C4×Dic13—21no—
141C4×Dic13—21no—
142#6099—42no—
143#6099—42no—
144C2×#1055—22no—
145C2×#1055—22no—
146C2×#1055—22no—
147C8×D13—44no—
148C2×#487D1311yescharacteristic, complemented
149#3079—131no—
150#3039—131no—
151C8×#41—131no—
152#1680—134no—
153#1679—134no—
154#1566—131no—
155#1549—131no—
156#1546—131no—
157C23×C13#12111yescharacteristic
158C22×D13—21no—
159Q8×C13—42no—
160Q8×C13—42no—
161Q8×C13—44no—
162Q8×C13—82no—
163Q8×C13—82no—
164C2×C4×C13—22no—
165C2×C4×C13—22no—
166C2×C4×C13—42no—
167C2×C4×C13—42no—
168C2×C4×C13—82no—
169C2×C4×C13—82no—
170C2×C4×C13#12111yescharacteristic
171C2×C4×C13#12111yescharacteristic
172C2×C4×C13#12111yescharacteristic
173C2×C4×C13C2×SD1612yes—
174C2×C4×C13#13512yes—
175C2×C4×C13C22×D411yescharacteristic
176C2×C4×C13C22×D411yescharacteristic
177C2×C4×C13C2×#4111yescharacteristic
178C22⋊D13—24no—
179C2×Dic13—21no—
180C2×Dic13—21no—
181C2×Dic13—21no—
182D52—21no—
183D52C2×SD1612yes—
184C4×D13—24no—
185C4×D13—42no—
186C4×D13—42no—
187Dic26—21no—
188Dic26C2×SD1612yes—
189C8×C13—22no—
190C8×C13—22no—
191#1055—42no—
192#1055—42no—
193#1055—42no—
194C2×#137—261no—
195C2×C4⋊Q8C2×D1311yescharacteristic
196C2×C4⋊Q8C2×D1311yescharacteristic
197C4×#41—131no—
198#487—21no—
199#487—21no—
200#487C2×D1314yes—
201#477—261no—
202#476—261no—
203#475—132no—
204#474—132no—
205#462—132no—
206#462—261no—
207#461—132no—
208#461—261no—
209C8×Q8—132no—
210C8×D4—132no—
211C8×D4—262no—
212#431—131no—
213#431—261no—
214#428—261no—
215#423—131no—
216#423—131no—
217#419—261no—
218#417—261no—
219C2×#103—22no—
220C2×C4×C8—261no—
221C2×C4×C8C2×D1311yescharacteristic
222#334—134no—
223#332—134no—
224#332—134no—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13#46512yes—
228C22×C13C2×#12111yescharacteristic
229C2×D13—22no—
230C2×D13—41no—
231C2×D13—41no—
232C4×C13—21no—
233C4×C13—21no—
234C4×C13—82no—
235C4×C13—82no—
236C4×C13#46512yes—
237C4×C13#47312yes—
238C4×C13C22×SD1611yescharacteristic
239C4×C13C2×#13511yescharacteristic
240C4×C13#57512yes—
241Dic13—22no—
242Dic13—41no—
243Dic13—41no—
244C2×#41—131no—
245C22×Q8—21no—
246C22×Q8—21no—
247#137—524no—
248C2×Q16—262no—
249C2×SD16—262no—
250C2×M16—261no—
251C2×M16—261no—
252C22×C8—262no—
253C22×C8C22⋊D1312yes—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8C22×D1312yes—
261C4⋊Q8C22×D1312yes—
262C4×Q8—131no—
263C4×Q8—131no—
264C4×D4—131no—
265C4×D4—131no—
266C4×D4—261no—
267C4×D4—261no—
268#117—131no—
269#117—261no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C42—261no—
275C2×C42C22×D1311yescharacteristic
276#107—262no—
277#106—262no—
278C4⋊C8—132no—
279C4⋊C8—132no—
280C4⋊C8—132no—
281C4⋊C8—262no—
282C4⋊C8—261no—
283C4⋊C8—261no—
284#103—24no—
285#103—24no—
286#103—262no—
287#103—262no—
288#103—262no—
289#102—262no—
290C22⋊C8—261no—
291C22⋊C8—262no—
292C4×C8—262no—
293C4×C8—261no—
294C4×C8C22⋊D1311yescharacteristic
295C4×C8C22⋊D1311yescharacteristic
296C4×C8C22×D1312yes—
297C2×C13—22no—
298C2×C13#304011yescharacteristic
299C2×C13C2×#46511yescharacteristic
300C2×C13C2×#47311yescharacteristic
301D13—42no—
302#41—134no—
303#41—262no—
304C2×Q8—22no—
305C2×Q8—22no—
306C2×Q8—44no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—42no—
310C2×Q8—42no—
311C2×Q8—131no—
312C2×D4—131no—
313C2×D4—261no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—261no—
317C22×C4—261no—
318C22×C4—261no—
319C22×C4D4×D1311yescharacteristic
320C22×C4#612911yescharacteristic
321C22×C4C2×C22⋊D1311yescharacteristic
322Q16—524no—
323SD16—524no—
324M16—522no—
325M16—522no—
326C2×C8—42no—
327C2×C8—262no—
328C2×C8—262no—
329C2×C8—262no—
330C2×C8—524no—
331C2×C8C2×C22⋊D1312yes—
332C2×C8C2×C22⋊D1312yes—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—131no—
342C4⋊C4—131no—
343C4⋊C4—261no—
344C4⋊C4—261no—
345C22⋊C4—261no—
346C22⋊C4—261no—
347C22⋊C4—261no—
348C42—261no—
349C42—261no—
350C42—261no—
351C42D4×D1311yescharacteristic
352C42#612911yescharacteristic
353C42C2×C22⋊D1311yescharacteristic
354C42C23×D1311yescharacteristic
355C13#1927511yescharacteristic, complemented, Sylow
356C23—261no—
357C23#8819211yescharacteristic
358Q8—42no—
359Q8—42no—
360Q8—44no—
361Q8—82no—
362Q8—82no—
363Q8—132no—
364Q8—261no—
365D4—132no—
366D4—264no—
367D4—261no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—82no—
373C2×C4—82no—
374C2×C4—261no—
375C2×C4—264no—
376C2×C4—261no—
377C2×C4—261no—
378C2×C4—522no—
379C2×C4—522no—
380C2×C4SD16×D1312yes—
381C2×C4#8817012yes—
382C2×C4#8819211yescharacteristic
383C2×C4#8819211yescharacteristic
384C2×C4#8819211yescharacteristic
385C2×C4C2×D4×D1311yescharacteristic
386C2×C4C2×#612911yescharacteristic
387C2×C4C22×C22⋊D1311yescharacteristic
388C8—22no—
389C8—22no—
390C8—522no—
391C8—522no—
392C8—522no—
393C22—21no—
394C22—21no—
395C22—262no—
396C22—521no—
397C22—521no—
398C22#1171883212yes—
399C22C2×#8819211yescharacteristic
400C4—21no—
401C4—21no—
402C4—82no—
403C4—82no—
404C4—262no—
405C4—521no—
406C4—521no—
407C4#1171883212yes—
408C4#1171885312yes—
409C4C2×SD16×D1311yescharacteristic
410C4C2×#8817011yescharacteristic
411C4#1171952712yes—
412C2—22no—
413C2—522no—
414C2#1312432611yescharacteristic
415C2C2×#1171883211yescharacteristic
416C2C2×#1171885311yescharacteristic
subgroupG/H
centerC22C2×#88192
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#487C2
socleC22×C13C2×#121
prime radicalC2×#6127D4
hypercenterC2×#487D13
hypocenterC13#19275
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #13114263C2semidirect
5. #13114256C2semidirect
6. #13113592C2semidirect
7. #13113521C2semidirect
8. #13113508C2semidirect
9. C2×C13×#487C2semidirect
148. C2×#487D13semidirect
355. C13#19275semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131246452
#131243192
C8×#61272
#131142632
#131142562
#131135922
#131135212
#131135082
C2×C13×#4872
#1927513